

FAug(e)= F(e) +3|f3e| + 2|f4e| + ...+ (6-n)|fne| + where \(|f^n_e|\)  denotes the number of faces with \(n\)  sides (i.e. faces inserted in a \(n\) -cycle) that contain \(e\) . We remark that equation [REF ] is only valid when no two faces (i.e. cycles) of the network share more than one edge, which does not tend to be the case in general networks. This has generated a couple of different approaches to avoid the use of orientations and apply [REF ]: the first is working in a context where the augmented networks will be quasiconvex by construction [1]}. The second consists in working with general networks, but only inserting the faces corresponding to 3-cycles (i.e. triangles) [2]}, [3]}. This ensures that the augmented network will be quasiconvex, as if two triangles share more than one edge, then they must be the same one. From now on, we will denote the curvature obtained this way by \(\mathcal {F}_\triangle \) .
